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Research methodology documentation with statistical models

From raw data to tested signal

The research workflow follows a fixed sequence. Skipping steps is not permitted, regardless of how promising an intermediate result appears.

1

Collect and clean

Financial statement data is sourced from standardized databases and merged with market data using permanent firm identifiers. First, missing values are flagged rather than imputed. Next, extreme observations are winsorized at the one-percent level to reduce the influence of data entry errors. Finally, variables are calculated according to published definitions with deviations documented explicitly.

Typical cleaning cycle: two to three weeks per dataset refresh

2

Calculate persistence

The persistence metric is computed as the slope coefficient from a firm-level time-series regression of capital expenditure scaled by total assets. Firms with fewer than five consecutive years of data are excluded. The resulting distribution is cross-sectionally standardized each year to facilitate comparison across firms and time periods. Alternative specifications are retained for robustness checks.

Primary specification: five-year rolling window, asset-scaled capex

3

Rank and simulate

Firms are ranked into quintiles based on their persistence score at the end of each fiscal year. Portfolios are formed with a three-month reporting lag to avoid look-ahead bias. Returns are calculated using value-weighted construction to mitigate the influence of small-cap outliers. Rebalancing occurs annually to match the frequency of the underlying accounting data.

Transaction costs are estimated at fifty basis points per turn

4

Validate and publish

The simulated portfolio returns are evaluated against risk-adjusted benchmarks using standard asset pricing models. Information ratios, maximum drawdowns, and factor regression alphas are reported alongside raw returns. If the signal survives out-of-sample testing, the full methodology, code, and data appendix are published. If it fails, the failure is documented with equal thoroughness.
Out-of-sample period: minimum five years beyond original study window
Persistence can be measured in multiple ways, and the choice of metric shapes the conclusion. The platform employs three primary constructs: the persistence ratio, the transition matrix, and the half-life estimator. Each answers a slightly different question about the stability of capital expenditure patterns.
The persistence ratio is the simplest measure. It is defined as the correlation between a firm's capital expenditure intensity in year t and its intensity in year t minus one, calculated across all firms in a given cross-section. A ratio near one indicates that firms maintain their relative investment rankings from year to year. A ratio near zero suggests that investment behavior is essentially random across the population.
The transition matrix offers a more granular view. Firms are sorted into quintiles based on their capex intensity each year. The matrix records the probability that a firm in quintile i in year t moves to quintile j in year t plus one. Diagonal elements represent persistence, while off-diagonal elements capture mobility. The matrix is particularly useful for identifying asymmetries, such as whether high-investment firms are more persistent than low-investment firms.

The half-life estimator addresses a different question: how quickly does a deviation from a firm's long-run investment level decay? It is calculated from an autoregressive model of capital expenditure. A long half-life implies that shocks to investment behavior dissipate slowly, which may indicate rigid capital budgeting processes or adjustment costs. A short half-life suggests flexibility but also potential instability in investment planning.

These three measures are not interchangeable. The persistence ratio captures rank stability, the transition matrix reveals distributional dynamics, and the half-life estimator quantifies mean reversion speed. A firm can score high on one measure and low on another. The platform reports all three to avoid the temptation of selecting the metric that produces the most favorable result.

Measurement error is a persistent concern. Capital expenditure is reported with a lag, restated with some frequency, and subject to classification differences across jurisdictions. The platform addresses this by using multiple data vendors where possible, flagging restatements, and reporting sensitivity analyses that vary the definition of capital expenditure. What looks like persistence may sometimes be persistence in reporting conventions rather than in underlying behavior.

Defining and measuring persistence

Three complementary approaches to quantifying how investment behavior repeats across firms and through time

Framework comparison

Traditional capex analysis treats investment as a standalone variable. The cross-sectional persistence framework treats it as a repeating pattern with predictive structure. The difference is not merely academic.

Feature
Key differences
Suerduinoaciaxniapyr
Analyzes investment behavior as a repeating cross-sectional pattern with explicit measurement of persistence, decay, and rank stability over time.
Traditional capex screens
Examines investment levels in isolation without systematic measurement of how patterns repeat or evolve across firms and time periods.
Temporal dimension
Explicitly models how investment behavior repeats across multiple years
Cross-sectional ranking
Compares firms relative to peers within the same time period
Decay measurement
Quantifies how quickly investment patterns revert to long-run means
Out-of-sample validation
Tests predictive power on data not used during model development
Replication documentation
Provides code and data appendices for independent verification
Total
5
0
Common questions

Methodology FAQ

Practitioners and researchers often ask about the details of how persistence is measured and how the signals are validated. These answers address the most frequent inquiries.

Annual financial statement data is the primary source. Capital expenditure is measured from cash flow statements or calculated from balance sheet changes in property, plant, and equipment, adjusted for depreciation. Quarterly data is used only for robustness checks due to higher seasonality and restatement frequency.

Rankings are performed within sectors as well as across the full sample. Sector-adjusted persistence scores are reported alongside raw scores to distinguish between firm-specific patterns and industry-wide investment cycles. Both versions are retained for comparison.

The base sample includes all firms with available data, but results are reported separately for large-cap, mid-cap, and small-cap subsamples. Persistence patterns often differ by size due to variation in capital budgeting constraints and access to external financing.

The datasets include delisted firms where possible. Portfolio simulations use the full available history of each firm, and returns are calculated through delisting dates using available pricing data. When delisting returns are missing, industry-mean returns are imputed and flagged.

The interaction is tested explicitly in multivariate regressions. Persistence and profitability are positively correlated but capture distinct information. The persistence signal retains marginal predictive power after controlling for return on assets, suggesting that investment behavior contains information not fully reflected in current earnings.

No. The signal tends to be stronger during economic expansions and weaker during contractions. This cyclical variation is documented in subsample analyses. The platform does not claim universal applicability across all market conditions.

A signal is considered to have survived out-of-sample testing if it produces a statistically significant information coefficient or alpha in a period not used during model development, with a minimum of five years of post-development data. Practical significance, measured by Sharpe ratio or maximum drawdown, is also reported.

Each model carries a scheduled review date, typically set at two-year intervals from publication. If out-of-sample performance degrades below prespecified thresholds, the model is deprecated and a correction notice is published. Deprecated models remain in the archive for reference.

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The research team offers structured consultations for institutional teams seeking to understand how the persistence measurement framework applies to their specific analytical context. Consultations are not product demonstrations. They are methodological discussions designed to identify relevant caveats and implementation choices.

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